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Fix spring impulse control
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centauri
parent
f370e3f841
commit
cf58410b89
3 changed files with 131 additions and 93 deletions
102
src/spring.luau
102
src/spring.luau
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@ -9,6 +9,7 @@ local update_descendants = graph.update_descendants
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local push_scope_as_child_of = graph.push_scope_as_child_of
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local UPDATE_RATE = 120
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local TOLERANCE_FACTOR = 10_000
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type Animatable = number | CFrame | Color3 | UDim | UDim2 | Vector2 | Vector3
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@ -24,7 +25,8 @@ type SpringState<T> = {
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k: number, -- spring constant
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c: number, -- damping coeff
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x0_123: vector, x0_456: vector, -- current position
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x0_123: vector, x0_456: vector, -- initial position
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x_123: vector, x_456: vector, -- current position
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x1_123: vector, x1_456: vector, -- target position
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v_123: vector, v_456: vector, -- current velocity
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@ -135,10 +137,8 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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local owner = assert_stable_scope()
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-- https://en.wikipedia.org/wiki/Damping
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local w_n = 2*math.pi / (period or 1)
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local z = damping_ratio or 1
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local k = w_n^2
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local c_c = 2*w_n
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local c = z * c_c
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@ -154,10 +154,12 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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c = c,
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x0_123 = vector.zero,
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x_123 = vector.zero,
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x1_123 = vector.zero,
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v_123 = vector.zero,
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x0_456 = vector.zero,
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x_456 = vector.zero,
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x1_456 = vector.zero,
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v_456 = vector.zero,
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@ -175,11 +177,10 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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end
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local updater = create_node(owner, updater_effect, false :: any)
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evaluate_node(updater)
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-- set initial position to goal
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data.x0_123, data.x0_456 = data.x1_123, data.x1_456
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data.x_123, data.x_456 = data.x1_123, data.x1_456
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-- set output to goal
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output.cache = data.source_value
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@ -190,7 +191,9 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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local dv = p.impulse
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if x then
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data.x0_123, data.x0_456 = type_to_vec6[typeof(x)](x)
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local x_123, x_456 = type_to_vec6[typeof(x)](x)
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data.x_123, data.x_456 = x_123, x_456
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data.x0_123, data.x0_456 = x_123, x_456
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end
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if v then
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@ -203,6 +206,7 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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data.v_456 += dv_456
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end
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-- schedule spring
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springs[data] = output
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end :: SpringSettings<T>
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@ -214,7 +218,7 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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-- set current position to value
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local v = ... :: T
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data.x0_123, data.x0_456 = type_to_vec6[typeof(v)](v)
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data.x_123, data.x_456 = type_to_vec6[typeof(v)](v)
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-- reset velocity
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data.v_123 = vector.zero
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@ -230,38 +234,29 @@ local function spring<T>(source: () -> T, period: number?, damping_ratio: number
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end, config
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end
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-- luau vectors have f32 for each component, unlike luau number which is f64
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local FLOAT32_MANTISSA_BITS = 23
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type float32 = number
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local function get_min_step(x: float32)
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local _,exponent = math.frexp(x)
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local lower_mantissa = math.ldexp(1, -FLOAT32_MANTISSA_BITS - 1)
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return math.ldexp(lower_mantissa, exponent)
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-- calculates a float tolerance, based on the magnitude of the float
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local function get_min_step(x: number): number
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return x/TOLERANCE_FACTOR
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end
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local function get_min_vector_step(goal: vector): vector
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local function get_min_vector_step(direction: vector): vector
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return vector.create(
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get_min_step(goal.x),
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get_min_step(goal.y),
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get_min_step(goal.z)
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get_min_step(direction.x),
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get_min_step(direction.y),
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get_min_step(direction.z)
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)
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end
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local function step_springs(dt: number)
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for data in springs do
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local k, c,
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x0_123, x1_123, u_123,
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x0_456, x1_456, u_456 =
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data.k, data.c,
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data.x0_123, data.x1_123, data.v_123,
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data.x0_456, data.x1_456, data.v_456
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if x0_123 == x1_123 and x0_456 == x1_456 then continue end
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for s in springs do
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local k = s.k
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local c = s.c
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local x_123, x_456 = s.x_123, s.x_456
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local x1_123, x1_456 = s.x1_123, s.x1_456
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local u_123, u_456 = s.v_123, s.v_456
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-- calculate displacement from target
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local dx_123 = x0_123 - x1_123
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local dx_456 = x0_456 - x1_456
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local dx_123 = x_123 - x1_123
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local dx_456 = x_456 - x1_456
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-- calculate spring force
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local fs_123 = dx_123*-k
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@ -271,35 +266,46 @@ local function step_springs(dt: number)
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local ff_123 = u_123*-c
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local ff_456 = u_456*-c
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-- calculate acceleration step
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local dv_123 = (fs_123 + ff_123)*dt
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local dv_456 = (fs_456 + ff_456)*dt
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-- calculate acceleration
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local a_123 = (fs_123 + ff_123)
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local a_456 = (fs_456 + ff_456)
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-- apply acceleration step
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local v_123 = u_123 + dv_123
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local v_456 = u_456 + dv_456
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-- step acceleration
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local v_123 = u_123 + a_123*dt
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local v_456 = u_456 + a_456*dt
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-- guarantee pos < pos + velocity <= goal
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local a_123 = vector.max(get_min_vector_step(x0_123), vector.abs(v_123) * dt) * vector.sign(v_123)
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local a_456 = vector.max(get_min_vector_step(x0_456), vector.abs(v_456) * dt) * vector.sign(v_456)
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-- step velocity
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local y_123 = x_123 + v_123*dt
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local y_456 = x_456 + v_456*dt
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-- calculate new position
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local x_123 = x0_123 + a_123
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local x_456 = x0_456 + a_456
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data.x0_123, data.x0_456 = x_123, x_456
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data.v_123, data.v_456 = v_123, v_456
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s.x_123, s.x_456 = y_123, y_456
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s.v_123, s.v_456 = v_123, v_456
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end
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end
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local function update_spring_sources()
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for data, output in springs do
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local x0_123, x0_456 = data.x0_123, data.x0_456
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if x0_123 == data.x1_123 and x0_456 == data.x1_456 then
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local x_123, x_456 = data.x_123, data.x_456
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local x1_123, x1_456 = data.x1_123, data.x1_456
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local v_123, v_456 = data.v_123, data.v_456
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local tol_123 = vector.abs(get_min_vector_step(x0_123 - x1_123))
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local tol_456 = vector.abs(get_min_vector_step(x0_456 - x1_456))
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if
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-- position is at goal (within tolerance)
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vector.max(vector.abs(x_123 - x1_123), tol_123) == tol_123
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and vector.max(vector.abs(x_456 - x1_456), tol_456) == tol_456
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-- velocity is at 0 (within tolerance)
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and vector.max(vector.abs(v_123/10), tol_123) == tol_123
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and vector.max(vector.abs(v_456/10), tol_456) == tol_456
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then
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springs[data] = nil
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output.cache = data.source_value
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else
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output.cache = vec6_to_type[typeof(data.source_value)](x0_123, x0_456)
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output.cache = vec6_to_type[typeof(data.source_value)](x_123, x_456)
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end
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update_descendants(output)
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